Symbolic images and invariant measures of dynamical systems

Ergodic Theory and Dynamical Systems

Volumn 30, Issue 4, 2010, Pages 1217-1237

  Osipenko, George ^a  

^a PETER THE GREAT ST PETERSBURG POLYTECHNIC UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77955802927     PISSN: 01433857     EISSN: 14694417     Source Type: Journal    
DOI: 10.1017/S0143385709000431     Document Type: Article

References (17)

1. M. Blank, G. Keller and C. Liverani. Ruelle-Perron-Frobenius spectrum for Anosov maps. Nonlinearity 15 (2002), 1905-1973.
2. L. M. Bregman. Relaxation method for determination of the common point of the convex sets and its application to problems of convex programming. J. Comput. Math. Math. Phys. 7(3) (1967), 630-631.
3. M. Dellnitz and O. Junge. On the approximation of complicated dynamical behavior. SIAM J. Numer. Anal. 36(2) (1999), 491-515.
4. J. Ding and A. Zhou. Finite approximation of Frobenius-Perron operators, a solution of Ulam's conjecture to multi-dimensional transformation. Phys. D 92(1-2) (1996), 61-66.
5. G. Froyland. Finite approximation of Sinai-Bowen-Ruelle measures for Anosov systems in two dimensions. Random and Computational Dynamics 3(4) (1995), 251-263.
6. G. Froyland. Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal. 32(7) (1998), 831-860.
7. G. Froyland. Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity 12 (1999), 79-101.
8. K. Ikeda. Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system. Opt. Comm. 30 (1979), 257-261.
9. A. Katok and B. Hasselblatt. Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press, Cambridge, 1995.
10. N. Kryloff and N. Bogollouboff. La theorie generale De La mesure dans son application a l'etude das systemes dynamiques De La mecanique non lineaire. Ann. of Math. 38(1) (1937), 65-113.
11. D. Lind and B. Marcus. An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge, 1995.
12. G. Osipenko. On a symbolic image of dynamical system. Boundary Value Problems. Interuniv. Collect. Sci. Works, Perm State Technical University, Perm, 1983, 101-105.
13. G. Osipenko. Numerical explorations of the Ikeda mapping dynamics. Electron J. Differential Equations and Control Processes 2 (2004), 43-67. http://www.neva.ru/journal.
14. G. Osipenko. Dynamical Systems, Graphs, and Algorithms (Lecture Notes in Mathematics, 1889). Springer, Berlin, 2007.
15. G. V. Sheleikhovsky. Composition of city plan as a transport problem. Manuscript, 1946.
16. L. Tien-Yien. Finite approximation for the Frobenius-Perron operator, a solution to Ulam's conjecture. J. Approx. Theory 17 (1976), 177-186.
17. S. Ulam. Problems in Modern Mathematics. Interscience, New York, 1960.